ECE Microwave Engineering

Transcription

1 ECE Microwave Engineering Fall 8 Prof. David R. Jackson Dept. of ECE Adapted from notes by Prof. Jeffery T. Williams Notes Power Dividers and Circulators

2 Power Dividers and Couplers A power divider is used to split a signal. A coupler is used to combine a signal. Divider Coupler (Combiner) These are examples of a three-port network.

3 Three Port Networks General 3-port network: [ ]

4 Three Port Networks (cont.) If all three ports are matched, and the device is reciprocal and lossless, we have: 3 3 [ ] 3 3 (The matrix is also unitary.) (There are three distinct values.) This is not physically possible! (see next slide) 4

5 Power Dividers and Couplers (cont.) 3 3 [ ] 3 3 Lossless, reciprocal, and matched at all ports is not physically possible. Lossless [] is unitary Hence: These cannot all be satisfied. (If only one is nonzero, we cannot satisfy all three.) At least of 3,, 3 must be zero. (If only one is zero (or none is zero), we cannot satisfy all three.) 5

6 Power Dividers T-Junction: lossless divider Y in Y in To match : Note, however, Y Thus, Y in 3 in Also, Y in 3 Y in If we match at port, we cannot match at the other ports! 6

7 Power Dividers (cont.) Assuming port matched: P in V V P P out out V V P P in in P P out3 out 3 We can design the splitter to control the powers into the two output lines. 7

8 Power Dividers (cont.) Examine the reflection at each port ( ii ): V / V V + + / V a a a a in V 3 in 3 3 ( zero if port is matched) V V a a 3 a a V Note: A match on port requires < < 3 (since the two output lines combine in parallel), 33 8

9 Power Dividers (cont.) Also, we have: V V + a a V / V V / V V / V Also ( ) / / ( ) V V + V V Hence + ( ) imilarly: + ( ) ( )

10 Power Dividers (cont.) If port is matched: ; ; ( + ) ( + ) [ ] ( ) Only The output ports and 3 are not isolated.

11 Power Dividers (cont.) ummary P P out3 out 3 ; ; ( ) The input port is matched, but not the output ports. The output ports are not isolated. Waves reflected from devices on ports and 3 with cause interference with the other devices.

12 Power Dividers (cont.) Example: Microstrip T-junction power divider 33 5 [ Ω] [ Ω] [ Ω] 3 3 Incident 3 [ Ω] 3 3 Note: Quarter-wave transformers could be put on the output lines to bring the final output lines back to 5 [Ω].

13 Power Dividers (cont.) The matched power divider also works as a match power combiner 33 5 [ Ω] [ Ω] [ Ω] outgoing b a + a a ( ) a3 + 3 [ Ω] Equal waves are incident from ports and 3 (a a 3 ). There is no reflection if equal waves are incident on ports and 3. 3

14 Wilkenson Power Divider Equal-split (3 db) power divider (The Wilkenson can also be designed to have an unequal split.) All ports matched ( 33 ) 3 Output ports are isolated ( 3 3 ) Note: No power is lost in going from port to ports and 3: 3 [ ] j Obviously not unitary The derivation is in the appendix. 4

15 Wilkenson Power Divider (cont.) [ ] j λ g /4 33 λ g /4 3 3 All three ports are matched, and the output ports are isolated. 5

16 Wilkenson Power Divider (cont.) [ ] j λ g /4 3 j λ g /4 3 j When a wave is incident from port, half of the total incident power gets transmitted to each output port (no loss of power). When a wave is incident from port or port 3, half of the power gets transmitted to port and half gets absorbed by the resistor, but nothing gets through to the other output port (the two output ports are isolated from each other). 6

17 Wilkenson Power Divider (cont.) Example: Microstrip Wilkenson power divider 5 [ Ω] 5 [ Ω] T 7.7 [ Ω] T 7.7 [ Ω] R [ Ω] 3 5 [ Ω] 7

18 Wilkenson Power Divider (cont.) Figure 7.5 of Pozar Photograph of a four-way corporate power divider network using three microstrip Wilkinson power dividers. Note the isolation chip resistors. Courtesy of M.D. Abouzahra, MIT Lincoln Laboratory. 8

19 Wilkenson Power Divider (cont.) Figure 7. of Pozar Frequency response of an equal-split Wilkinson power divider. Port is the input port; ports and 3 are the output ports. 9

20 Circulators Now consider a 3-port network that is non-reciprocal, with all ports matched, and is lossless: 3 [ ] (There are six distinct values.) Circulator These equations will be satisfied if: Lossless or Note that ij ji. 3 3

21 Circulators (cont.) [ ] Note: We have assumed here that the phases of all the parameters are zero. Clockwise (LH) circulator 3 [ ] Circulators can be made using biased ferrite materials. 3 Counter-clockwise (RH) circulator

22 Circulators (cont.) Application: Wireless system TX Antenna Transmitter TX 3 RX RX Receiver The same antenna can be used for transmit and receive. The transmit and receive frequencies can even be the same.

23 Circulators (cont.) Note: A duplexer (diplexer) can be used to transmit and receive two different channels with the same antenna, if the frequencies are separated enough. Transmitter f T f T Duplexer Receiver f R f R Antenna A duplexer is a type of filter that combines or splits two signals at different frequencies. 3

24 Circulators (cont.) An example of a duplexer: 4

25 Circulators (cont.) Isolator: Out In 3 Matched load A signal from the input port goes to the output port. A signal from the output port does not get to the input port. 5

26 Circulators (cont.) A waveguide-based circulator with a matched load at port 3, acting as an isolator 6

27 Appendix The analysis of the Wilkinson power divider is given here. Even and odd analysis is used to analyze the structure when port is excited. To determine, 3 Only even analysis is needed to analyze the structure when port is excited. To determine, The other components can be found by using symmetry and reciprocity. 7

28 Appendix (cont.) Top view Plane of symmetry A microstrip realization is shown. plit structure along plane of symmetry (PO) Even voltage even about PO place OC along PO Odd voltage odd about PO place C along PO 8

29 Appendix (cont.) Plane of symmetry How do you split a transmission line? (This is needed for the even case.) Voltage is the same for each half of line (V) Current is halved for each half of line (I/) V I Top view h I / PO I / (magnetic wall) microstrip line For each half 9

30 Appendix (cont.) Port Excitation even problem Note: The resistor has been split into two resistors in series. Ports and 3 are excited in phase., 3 Note : V V e e 3 3

31 Appendix (cont.) Port Excitation odd problem Note: The resistor has been split into two resistors in series. Ports and 3 are excited 8 o out of phase., 3 Note : V, V V o o o 3 3

32 Appendix (cont.) Port Excitation even problem λ g /4, e e in e V + V + V e Port e +V OC ( ) e in e in e in + e Recall: in T (quarter-wave transformer) L Also, by symmetry, e 33 Also, e e 3 3

33 Appendix (cont.) Port Excitation odd problem Port o V hort o in o o in o in + Also, by symmetry, o 33 Also, o o 3 33

34 V V + V V + V e o ( + ) ( + ) e o e o V V + V V a a 3 e o e o V V + V V a a 3 Appendix (cont.) We add the results from the even and odd cases together: 33 3 (by symmetry) V V V V V e o ( ) ( ) (by reciprocity) Note: ince all ports have the same, we ignore the normalizing factor in the parameter definition. In summary, for port excitation, we have:

35 Appendix (cont.) Port Excitation Port When port is excited, the response, by symmetry, is even. (Hence, the total fields are the same as the even fields.) 35

36 Appendix (cont.) Even Problem Top view Port V + V λ g /4 O.C. symmetry plane V +e + V e λ g /4 OC λ g /4 V V, V V + e + e I V I e V e / PMC e I microstrip line # I 36

37 Port Excitation even problem Appendix (cont.) Port ( ) e in e e in e in+ Recall: in T (quarter-wave transformer) L V V e e + + e V V a a a 3 Hence 37

38 Appendix (cont.) Port Excitation even problem V e e + + e V V a a a a V 3 3 Port V +e V e V e V V e e ( ) V V + V e + e e + e e e + e e V (reciprocal) ( +Γ) ( Γ) e V V j j V j Along λ g /4 wave transformer: + β + β ( ) ( +Γ ) V z V e e e j z j z z + ( ) ( ) V V V +Γ e + ( λg /4) ( ) V V V j Γ e Γ distance from port

39 For the other components: Appendix (cont.) By symmetry: By reciprocity: j j We then have the final matrix: [ ] j 39